{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fluid Logo\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/grids/Fluid_Logo.ipynb)\n",
    "\n",
    "\n",
    "This example shows how to run a simple fluid simulation with inflows and obstacles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's begin by defining the resolution and size of our domain, as well as the obstacle geometries.\n",
    "We build a complex obstacle geometry out of multiple boxes here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain = dict(x=128, y=128, bounds=Box(x=100, y=100))\n",
    "geometries = [Box(x=(15 + x * 7, 15 + (x + 1) * 7), y=(41, 83)) for x in range(1, 10, 2)] + [Box['x,y', 43:50, 41:48], Box['x,y', 15:43, 83:90], Box['x,y', 50:85, 83:90]]\n",
    "geometry = union(geometries)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the obstacle! For the right plot, we sample the geometry on a grid matching our simulation settings. The simulation will only use the sampled version. If you have thin geometries, make sure that they don't result in holes after resampling!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(geometry, CenteredGrid(geometry, 0, **domain))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define three smoke inflows for our simulation and sample them on a grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "inflow = CenteredGrid(Box(x=(14, 21), y=(6, 10)), ZERO_GRADIENT, **domain) + \\\n",
    "         CenteredGrid(Box(x=(81, 88), y=(6, 10)), ZERO_GRADIENT, **domain) * 0.9 + \\\n",
    "         CenteredGrid(Box(x=(44, 47), y=(49, 51)), ZERO_GRADIENT, **domain) * 0.4\n",
    "plot(inflow)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we define the simulation.\n",
    "We let the smoke apply an upwards `buoyancy_force` on the velocity proportional to its density.\n",
    "As we sample the velocity on a staggered grid but the smoke density on a centered grid, we need to resample the force to the staggered grid.\n",
    "Passing the obstacle to `make_incompressible` ensures that that no fluid can flow into or out of the defined geometry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit_compile\n",
    "def step(smoke, v, pressure, inflow, dt=1.):\n",
    "    smoke = advect.semi_lagrangian(smoke, v, 1) + inflow\n",
    "    buoyancy_force = resample(smoke * (0, 0.1), to=v)\n",
    "    v = advect.semi_lagrangian(v, v, 1) + buoyancy_force\n",
    "    v, pressure = fluid.make_incompressible(v, geometry, Solve('CG-adaptive', 1e-5, x0=pressure))\n",
    "    return smoke, v, pressure\n",
    "\n",
    "v0 = StaggeredGrid(0, boundary=0, **domain)\n",
    "smoke0 = CenteredGrid(0, boundary=ZERO_GRADIENT, **domain)\n",
    "smoke_trj, v_trj, pressure_trj = iterate(step, batch(time=200), smoke0, v0, None, inflow=inflow)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that passing `batch(time=200)` to `iterate` stacks the variables along a new dimension called `time`.\n",
    "This allows us to easily animate the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x1d3399bab50>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(smoke_trj.time[::2], animate='time')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}
